What is the correlation between mortgage rates and home sale numbers?

The correlation between these two numbers is that, all other things being equal, the number of home sales will tend to go up as the mortgage rates go down. In other words, there will tend to be a negative correlation between the two.

The reason for this is that the mortgage rate is effectively a part of the price of a home. Most people who buy houses cannot buy them outright and must instead take out a mortgage to pay for the house. The law of demand tells us that when the price of a good or service goes up, the quantity demanded will (all other things being equal) go down. This means that when mortgage rates go up, the number of home sales will go down.